What exactly defines a single or double braced throne? I'm pretty sure a single braced throne means that each leg is only one ply/unit/strut/what ever you want to call it (single brace) and a double brace means each leg is 2 plies/units (double brace). Am I getting this right?

I am a bit confused, because there are some listings online that are advertised as single braced, but the picture shows the legs as being double braced. Is this just an error on the website? Example below:

You are correct. Double-bracing refers to the legs being double braced. They've made a mistake in their listing of the product.

Double bracing for a throne is good but in a reality, you need a spindle that controls the height of the throne. Because of the added weight of this mechanism, most all thrones will be double-braced anyway. But I would totally avoid thrones that did not have a spindle controlling the height adjustment because you need to lock it from spinning.

You are correct. Double-bracing refers to the legs being double braced. They've made a mistake in their listing of the product.

Double bracing for a throne is good but in a reality, you need a spindle that controls the height of the throne. Because of the added weight of this mechanism, most all thrones will be double-braced anyway. But I would totally avoid thrones that did not have a spindle controlling the height adjustment because you need to lock it from spinning.